The Newton-Wigner localization concept and noncommutative space

Abstract

In the formulation of the Newton-Wigner postulates for the relativistic localized states the hypothesis of commutativity of the position operator components is silently accepted as an evident fact. In the present work it is shown that commutativity is not necessary condition and the alternative (noncommutative) approach to the relativistic position operator and localization concept can be realized in a framework of the physically as well as mathematically comprehensive scheme.